Hi there,
"
If k is an integer and 5^k < 20,000, what is the greatest possible value of k?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
"
Intuitively I though I should turn 20,000 into 2^5 * 5^4, and since 2^5 is 32, k shouldn’t exceed 6 if 5^k is to be less than 20,000. However, even though I was able to find the correct choice, I still can’t articulate why this question can be solved in this way. I can’t breakdown the question and figure out what the question is asking in essence. Can anyone help me lay out a clearer thought process for solving this?
Thank you!